NDLI: Uniformly Hyperarchimedean Lattice-Ordered Groups

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Uniformly Hyperarchimedean Lattice-Ordered Groups

Content Provider	Springer Nature Link
Author	Hager, Anthony W. Kimber, Chawne M.
Copyright Year	2007
Abstract	An abelian ℓ-group with strong unit ( $\mathcal{\mathcal{L}}_1 $ -object) G is hyperarchimedean (HA) iff G ≤ C(YG) (the ℓ-group of real continuous functions on the maximal ideal space, YG) with λ(g) = inf{ ∣ g(x) ∣ ≠ 0} > 0 for each 0 ≠ g ∈ G. In case inf{λ(g):0 ≠ g ∈ G} > 0, we call G uniformly hyperarchimedean (UHA). This paper: examines the structure of the UHA groups in detail; shows that UHA solves the problem: when is an $\mathcal{\mathcal{L}}_1 $ -product HA?; describes completely the $\mathcal{\mathcal{L}}_1 $ − HSP-classes which are contained in HA. Final remarks detail the connection with MV-algebras.
Ending Page	131
Page Count	11
Starting Page	121
File Format	PDF
ISSN	01678094
e-ISSN	15729273
Journal	Order
Issue Number	2
Volume Number	24
Language	English
Publisher	Springer Netherlands
Publisher Date	2007-10-31
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometry Hyperarchimedean Convex and Discrete Geometry Ordered group Theory of Computation Algebraic properties of function spaces Many-valued logic Lattices of varieties Variety Ordered abelian groups, Riesz groups, ordered linear spaces
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Computational Theory and Mathematics Geometry and Topology

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